Unit 2: Valuing stocks and bonds
How much is a share or a bond worth, and why does that value change when the economy or interest rates change? Change any number on the left of a tool and every result, chart and explanation updates at once. Each tool starts from a worked example in the lecture notes, so you can check it against your notes and the video, then try your own numbers.
Chapter 9. Equity valuation
A share is worth the present value of the cash it will pay its owner. These tools value a stock from its dividends, show when growth adds value and when it destroys it, and value a whole firm from its free cash flow.
Dividend discount model
The intrinsic value of a share is the present value of the dividends (and eventual sale price) you expect, discounted at the required return k, the return investors need given the stock's risk. Compare it with the market price: if the value is higher, the stock is underpriced; if lower, it is overpriced. Pick a model to load its worked example.
Starts from Worked examples 9.1, 9.2, 9.4 and 9.5 (videos 09-1 and 09-2).
Growth: does it create or destroy value?
A firm that plows back (reinvests) part of its earnings grows, but growth only helps shareholders if the new investments are expected to earn a return on equity (ROE) above the return k they require. The price splits into the value of the firm with no growth plus the present value of growth opportunities (PVGO).
Starts from Worked examples 9.8 and 9.9 (video 09-3).
Free cash flow valuation
Many firms pay little or no dividend, so analysts value the free cash flow the business generates instead. Discount a few years of forecast cash flow, add the discounted terminal value (the value of everything after the forecast years, assuming steady growth), and you have the value of the firm or of its equity.
Starts from Worked examples 9.11 and 9.12 (video 09-4).
Chapter 11. Macroeconomic analysis and business cycles
The economy drives both the cash flows of firms and the interest rates used to discount them. This tool walks around a stylized business cycle and reads a central bank announcement the way the market does.
Business cycle and sector rotation
Economies move through expansions and contractions, turning at a peak (into recession) and at a trough (into recovery). Some economic series turn before the economy (leading indicators), some with it (coincident) and some after it (lagging). Pick a phase to see what each group is doing and which kinds of industries tend to do well, then read a Fed announcement.
Starts from Worked example 11.1 and the business cycles section (videos 11-1 and 11-2).
Chapter 12. Industry analysis
Industries differ in how strongly their profits respond to the business cycle. One big reason is how much of their costs are fixed.
Operating leverage
Fixed costs (rent, aircraft, plant) do not shrink when sales fall; variable costs (goods sold, fuel) do. The more of a firm's costs are fixed, the more its profit swings when sales change. The degree of operating leverage (DOL) measures how many percent profit changes for each 1% change in sales.
Starts from Worked example 12.1 (video 12-1).
Chapter 13. Bonds: prices and yields
A bond promises fixed payments: coupons and the face value at maturity. Its price is the present value of those payments, so it moves opposite to interest rates.
Bond pricer
Find a bond's price from its yield to maturity (YTM, the single discount rate that makes the present value of its payments equal its price), or switch the mode to find the YTM from a price. The face value is what is repaid at maturity; the coupon rate sets the yearly interest as a percentage of face value.
Starts from Worked example 13.10, and also reproduces 13.1, 13.5, 13.6 and 13.7 (videos 13-1, 13-3 and 13-4).
Quoted price and invoice price
Bond prices are quoted without the interest that has built up since the last coupon. If you buy between coupon dates you also pay the seller this accrued interest, because you will receive the whole next coupon. The invoice price is what you actually pay.
Starts from Worked examples 13.2 and 13.3 (video 13-2).
Pull to par
If the yield stays the same, every bond's price moves toward its face value as maturity approaches: a premium bond drifts down, a discount bond drifts up, a par bond stays put, and a zero-coupon bond (one that pays only the face value) climbs all the way from a deep discount.
Starts from Worked examples 13.11 and 13.9 (video 13-4).
Chapter 14. The yield curve and implied forward rates
Interest rates differ by maturity. Today's rates for different maturities imply the rates the market is locking in for future years.
Yield curve and forward rates
A spot rate is today's yield for lending from now until a given year. The forward rate for a future year is the rate that today's spot rates imply for that year alone. Under the expectations theory the forward rate is the market's forecast of that year's short rate; under the liquidity preference theory it is the forecast plus a liquidity premium for holding longer bonds.
Starts from Worked examples 14.1 and 14.2 (video 14-1).
Chapter 15. Interest-rate risk: duration and immunization
How much does a bond's price move when yields move, and how can a pension fund protect itself against that risk?
Duration and convexity
Macaulay duration is the average time until you receive a bond's value, weighting each payment by its share of the price. Modified duration turns it into a sensitivity: roughly the percentage price change for a one-point change in yield. Because the true price curve bends (convexity), the duration estimate is close for small yield changes and less accurate for large ones.
Starts from Worked examples 15.1 and 15.3, and also reproduces 15.4 (videos 15-2 and 15-3).
Immunization
A fund that must make known future payments can protect itself from interest-rate changes by holding bonds whose present value and duration both match those of the liability. Mixing a short and a long zero-coupon bond lets you hit any duration in between.
Starts from Worked example 15.6 (video 15-4).